AISM 52, 84-107

## A stochastic advection-diffusion model for the Rocky Flats soil plutonium data

### Jaroslav Mohapl

Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

(Received October 27, 1997; revised September 28, 1998)

Abstract.
An advection-diffusion equation with time and space dependent
random coefficients is derived as a model for the plutonium
concentration changes in the surface soil around the Rocky
Flats Plant northwest of Denver, Colorado. The equation is
used to fit a set of temporal-spatial data sampled annually
over a 23 year period from 71 sites around the plant. The
coefficients of the advection-diffusion equation are
derived from the estimated covariance function of the
observed random field using a combination of maximum
likelihood and quasi-likelihood techniques.
Goodness-of-fit of the model to the data is also
assessed. Finally we interpret the model in terms of the
advection-diffusion mechanism.

Key words and phrases:
Temporal-spatial data, temporal-spatial process, random field,
parameter estimation, stochastic partial differential equation,
stochastic modeling.

**Source**
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